common/math: optimized modexp (+ fuzzer) (#25525)

This adds a 
* core/vm, tests: optimized modexp + fuzzer

* common/math: modexp optimizations

* core/vm: special case base 1 in big modexp

* core/vm: disable fastexp

common/math/modexp.go

@@ -0,0 +1,82 @@
+// Copyright 2020 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math
+
+import (
+	"math/big"
+	"math/bits"
+
+	"github.com/ethereum/go-ethereum/common"
+)
+
+// FastExp is semantically equivalent to x.Exp(x,y, m), but is faster for even
+// modulus.
+func FastExp(x, y, m *big.Int) *big.Int {
+	// Split m = m1 × m2 where m1 = 2ⁿ
+	n := m.TrailingZeroBits()
+	m1 := new(big.Int).Lsh(common.Big1, n)
+	mask := new(big.Int).Sub(m1, common.Big1)
+	m2 := new(big.Int).Rsh(m, n)
+
+	// We want z = x**y mod m.
+	// z1 = x**y mod m1 = (x**y mod m) mod m1 = z mod m1
+	// z2 = x**y mod m2 = (x**y mod m) mod m2 = z mod m2
+	z1 := fastExpPow2(x, y, mask)
+	z2 := new(big.Int).Exp(x, y, m2)
+
+	// Reconstruct z from z1, z2 using CRT, using algorithm from paper,
+	// which uses only a single modInverse.
+	//	p = (z1 - z2) * m2⁻¹ (mod m1)
+	//	z = z2 + p * m2
+	z := new(big.Int).Set(z2)
+
+	// Compute (z1 - z2) mod m1 [m1 == 2**n] into z1.
+	z1 = z1.And(z1, mask)
+	z2 = z2.And(z2, mask)
+	z1 = z1.Sub(z1, z2)
+	if z1.Sign() < 0 {
+		z1 = z1.Add(z1, m1)
+	}
+
+	// Reuse z2 for p = z1 * m2inv.
+	m2inv := new(big.Int).ModInverse(m2, m1)
+	z2 = z2.Mul(z1, m2inv)
+	z2 = z2.And(z2, mask)
+
+	// Reuse z1 for m2 * p.
+	z = z.Add(z, z1.Mul(z2, m2))
+	z = z.Rem(z, m)
+
+	return z
+}
+
+func fastExpPow2(x, y *big.Int, mask *big.Int) *big.Int {
+	z := big.NewInt(1)
+	if y.Sign() == 0 {
+		return z
+	}
+	p := new(big.Int).Set(x)
+	p = p.And(p, mask)
+	if p.Cmp(z) <= 0 { // p <= 1
+		return p
+	}
+	if y.Cmp(mask) > 0 {
+		y = new(big.Int).And(y, mask)
+	}
+	t := new(big.Int)
+
+	for _, b := range y.Bits() {
+		for i := 0; i < bits.UintSize; i++ {
+			if b&1 != 0 {
+				z, t = t.Mul(z, p), z
+				z = z.And(z, mask)
+			}
+			p, t = t.Mul(p, p), p
+			p = p.And(p, mask)
+			b >>= 1
+		}
+	}
+	return z
+}